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Adjust Solve Parameters in the PDE Modeler App

To specify parameters for solving a PDE, select Parameters from the
Solve menu. The set of solve parameters differs depending on
the type of PDE. After you adjust the parameters, solve the PDE by selecting
Solve PDE from the Solve menu or
by clicking the button.

Elliptic Equations

By default, no specific solve parameters are used, and the elliptic
PDEs are solved using the basic elliptic solver assempde.
Optionally, the adaptive mesh generator and solver adaptmesh can
be used. For the adaptive mode, the following parameters are available:

Adaptive mode. Toggle the adaptive
mode on/off.

Maximum number of triangles.
The maximum number of new triangles allowed (can be set to Inf).
A default value is calculated based on the current mesh.

Maximum number of refinements.
The maximum number of successive refinements attempted.

Triangle selection method. There
are two triangle selection methods, described below. You can also
supply your own function.

Worst triangles. This method
picks all triangles that are worse than a fraction of the value of
the worst triangle (default: 0.5).

Function parameter. The function
parameter allows fine-tuning of the triangle selection methods. For
the worst triangle method (pdeadworst), it is the
fraction of the worst value that is used to determine which triangles
to refine. For the relative tolerance method, it is a tolerance parameter
that controls how well the solution fits the PDE.

If the problem is nonlinear, i.e., parameters in the PDE are
directly dependent on the solution u, a nonlinear
solver must be used. The following parameters are used:

Use nonlinear solver. Toggle
the nonlinear solver on/off.

Nonlinear tolerance. Tolerance
parameter for the nonlinear solver.

Initial solution. An initial
guess. Can be a constant or a function of x and y given
as a MATLAB® expression that can be evaluated on the nodes of
the current mesh.

Examples: 1, and exp(x.*y).
Optional parameter, defaults to zero.

Jacobian. Jacobian approximation
method: fixed (the default), a fixed point iteration, lumped,
a “lumped” (diagonal) approximation, or full,
the full Jacobian.

Norm. The type of norm used for
computing the residual. Enter as energy for an
energy norm, or as a real scalar p to give the lp
norm. The default is Inf, the infinity (maximum)
norm.

Note

The adaptive mode and the nonlinear solver can be used together.

Parabolic Equations

The solve parameters for the parabolic PDEs are:

Time. A MATLAB vector of
times at which a solution to the parabolic PDE should be generated.
The relevant time span is dependent on the dynamics of the problem.

Examples: 0:10, and logspace(-2,0,20)

u(t0). The initial value u(t0)
for the parabolic PDE problem The initial value can be a constant
or a column vector of values on the nodes of the current mesh.

Relative tolerance. Relative
tolerance parameter for the ODE solver that is used for solving the
time-dependent part of the parabolic PDE problem.

Absolute tolerance. Absolute
tolerance parameter for the ODE solver that is used for solving the
time-dependent part of the parabolic PDE problem.

Hyperbolic Equations

The solve parameters for the hyperbolic PDEs are:

Time. A MATLAB vector of
times at which a solution to the hyperbolic PDE should be generated.
The relevant time span is dependent on the dynamics of the problem.

Examples: 0:10, and logspace(-2,0,20).

u(t0). The initial value u(t0)
for the hyperbolic PDE problem. The initial value can be a constant
or a column vector of values on the nodes of the current mesh.

u'(t0). The initial value u˙(t0)
for the hyperbolic PDE problem. You can use the same formats as for u(t0).

Relative tolerance. Relative
tolerance parameter for the ODE solver that is used for solving the
time-dependent part of the hyperbolic PDE problem.

Absolute tolerance. Absolute
tolerance parameter for the ODE solver that is used for solving the
time-dependent part of the hyperbolic PDE problem.

Eigenvalue Equations

For the eigenvalue PDE, the only solve parameter is the Eigenvalue
search range, a two-element vector, defining an interval
on the real axis as a search range for the eigenvalues. The left side
can be -Inf.

Examples: [0 100], [-Inf 50]

Nonlinear Equations

Before solving a nonlinear elliptic PDE in the PDE Modeler app, select
SolveParameters. Then select
Use nonlinear solver and click
OK.

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